We see that the amount of information decreases as it is transmitted from lower to higher levels. This implies that at each level there is redundant information. Certainly, only non-redundant information has a cost, but the repeating of information, its redundancy, provides the reliability of its transmission defending it from errors and destruction of the text by noise. The redundancy of information at rth level of perception (or description) can be defined as (Klix, 1974)
where max T(r) = r log2n. For r = 0 the redundancy is defined as R(0) = 0. Then the corresponding redundancies in English will be equal to R(0) = 0, R(1) = 0.15, R(2) = 0.30 and R(3) = 0.35. The latter, for instance, implies that only 35% of letters are redundant at the third level, i.e. 65% of randomly distributed letters are sufficient for the understanding of the text. The cost of information can be defined as the degree of non-redundancy (Volkenstein, 1988):
Then for each level we have C(0) = 1, C(1) = 1.18, C(2) = 1.43, C(3) = 1.54.
We used here one of the simplest definitions of the cost of information. In fact, this problem "What is the cost of information?", in spite of continuing discussion, is still far from its completion. This discussion falls outside the framework of our book, but nevertheless we shall cite one example.
So, there is some aim. Let probabilities of its attainment before and after receiving information be equal to P0 and P1, respectively. Then the cost of information is equal to C = log2(P1/P0) (Kharkevich, 1963). However, if the aim is unattained without information (P0 = 0), then the cost of any finite information is equal to infinity. This is not properly understandable.
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